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Chapter 1: Sets (128 videos)

1.1: Revision
1. Set Definition
2. Problem-Set Definition
3. Set Notation & its Characteristics
4. Problem-Set Notation & its Characteristics
5. Definition & Notation of Some Important Sets
6. Order of a Set
7. Problem-Order of a Set
8. Interval Notation of a Set
 
1.2: A Few Definitions
1. Equal & Equivalent Sets
2. Problem 1: Equal & Equivalent Sets
3. Subset Definition
4. Problem 1: Subset Definition
5. Problem-Subset Definition
6. Proper Subset & Improper Subset
7. Problem 1: Proper Subset & Improper Subset
8. Properties of Subset
9. Problem 1: Properties of Subset
10. Power Set
11. Problem 1: Power Set
12. Universal Set
13. Introduction to Ordered Pairs
 
1.3: Operations on Sets
1. Union of Two Sets
2. Problem 1: Union of Two Sets
3. Exhaustive Sets and Cells
4. Intersection of Set
5. Problem 1: Intersection of Set
6. Difference of Sets
7. Problem 1: Difference of Sets
8. Symmetric Difference of two sets
9. Problem 1: Symmetric Difference of two sets
10. Complement of a Set
11. Problem 1: Complement of a Set
12. Double Complementation Law
13. Problem-Double Complementation Law
14. Cartesian Product of Sets
15. Problem 1: Cartesian Product of Sets
 
1.4: Properties of Operations on Sets
1. Commutative Law of Union of Sets
2. Problem 1: Commutative Law of Union of Sets
3. Commutative Law of Intersection of Sets
4. Problem 1: Commutative Law of Intersection of Sets
5. Intersection Associativity for Overlapping Sets
6. Problem 1: Intersection Associativity for Overlapping Sets
7. Intersection Associativity for Disjoint Sets
8. Problem 1: Intersection Associativity for Disjoint Sets
9. Intersection Associativity for Sets
10. More on Intersection Associativity for Sets
11. Problem 1: Intersection Associativity for Sets
12. Problem 1: More on Intersection Associativity for Sets
13. Union Associativity for Overlapping Sets
14. Problem 1: Union Associativity for Overlapping Sets
15. Union Associativity for Disjoint Sets
16. Problem 1: Union Associativity for Disjoint Sets
17. Union Associativity for Sets
18. Problem 1: Union Associativity for Sets
19. More on Union Associativity for Set
20. Problem 1: More on Union Associativity for Set
21. Distributivity of Union Over Intersection of Sets
22. Problem 1: Distributivity of Union Over Intersection of Sets
23. Distributivity of Intersection Over Union of Sets
24. Problem 1: Distributivity of Intersection Over Union of Sets
25. Introducing Field
26. Problem-Introducing Field
27. Distributive Property of Cartesian Product Over Union
28. Problem-Distributive Property of Cartesian Product Over Union
29. Distributive Property of Cartesian Product Over Intersection
30. Problem-Distributive Property of Cartesian Product Over Intersection
31. Distributive Property of Cartesian Product Over Difference
32. Problem-Distributive Property of Cartesian Product Over Difference
33. Identity With Respect to Intersection
34. Problem-Identity With Respect to Intersection
 
1.5: Some Important Laws
1. Identity Laws
2. Problem-Identity Laws
3. Laws of Complement
4. Problem-Laws of Complement
5. Some Important Laws
6. Problem-Some Important Laws
7. Demorgans Law for Overlapping Sets
8. Problem 1: Demorgans Law for Overlapping Sets
9. Demorgans Law for Disjoint Sets
10. Problem 1: Demorgans Law for Disjoint Sets
11. Demorgans Law for Set & its Subset
12. Problem 1: Demorgans Law for Set & its Subset
13. Introduction to Binary Relation
14. Problem-Introduction to Binary Relation
15. Problem 1: Introduction to Binary Relation
16. Domain & Range of Binary Relation
17. Problem 1: Domain & Range of Binary Relation
18. Problem-Domain & Range of Binary Relation
19. Introduction to Binary Operations
20. Problem-Introduction to Binary Operations
21. Multiplication Table
22. Problem-Multiplication Table
23. Operations on Residue Classes Modulo n
24. Problem-Operations on Residue Classes Modulo n
25. Properties of Binary Operations
26. Problem-Properties of Binary Operations
27. Theorems on Binary Operation
28. More on Theorems on Binary Operation
29. Problem-Theorems on Binary Operation
30. Introduction to Function
31. More on Introduction to Functions
32. Problem 1: Introduction to Function
33. Problem-Introduction to Function
34. Problem3-Introduction to Function
35. Problem4-Introduction to Function
36. Implied Domain
37. Finding Domain and Range of Functions
38. Types of Relations
39. Operations on Functions
40. Into Function
41. Problem 1: Into Function
42. Problem-Into Function
43. Onto Function
44. Problem 1: Onto Function
45. Problem-Onto Function
46. One to One Function
47. Problem 1: One to One Function
48. Problem-One to One Correspondence
49. Bijective Function
50. Problem 1: Bijective Function
51. Problem-Bijective Function
52. Injective Function
53. Problem 1: Injective Function
54. Problem-Injective Function
55. One-One Function
56. Problem-One-One Function
57. Set Builder Notation for a Function
58. Problem-Set Builder Notation for a Function
 

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